Find the zeros of the function. Enter the solutions from least to greatest. $f (x)=(x -3)(2x -8)$ $\text{lesser }x = $
Solution: For any two expressions $A$ and $B$ : If $A\cdot B=0$ then either $A=0$ or $B=0$. This is called the zero product property. In our case, $(x -3)(2x -8)=0$. So either $(x -3)=0$ or $(2x -8)=0$ : $\begin{aligned} (1)&&x -3&=0 \\\\ &&x&=3 \end{aligned}$ $\begin{aligned} (2)&&2x -8&=0 \\\\ &&2x &= 8 \\\\ &&x&=4 \end{aligned}$ In conclusion, $\begin{aligned} \text{lesser }x &= 3 \\\\ \text{greater } x &= 4 \end{aligned}$